Timeline for Nonsingular is rational singular
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| Jun 22, 2022 at 7:16 | history | edited | CommunityBot |
replaced http://front.math.ucdavis.edu/ with https://arxiv.org/abs/
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| Apr 3, 2014 at 18:31 | comment | added | Karl Schwede | There are proofs of Grauert-Riemenschneider vanishing in characteristic zero that certainly don't assume that $R f_* O_X = O_Y$. I think for instance you can see a proof on Page 186 of Lazarsfeld's book "Positivity in Algebraic Geometry II" | |
| Apr 3, 2014 at 0:47 | comment | added | Li Yutong | The theorem of Grauert-Riemenschneider vanishing I mentioned is on page 45 of the following book mi.fu-berlin.de/users/esnault/books/esvibuch.pdf | |
| Apr 3, 2014 at 0:45 | comment | added | Li Yutong | Thank you very much! I checked the Grauert-Riemenschneider vanishing. However, it use the fact ${\rm R}f_* \mathcal{O}_X = \mathcal{O}_X \in D(X)$ as the first step towards the proof. Moreover, it says that ${\rm R}f_* \mathcal{O}_X = \mathcal{O}_X$ follows from Leray spectral sequence. I was wondering if there was a direct proof using Leray spectral sequence? | |
| Apr 2, 2014 at 16:05 | history | answered | Karl Schwede | CC BY-SA 3.0 |